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Hecke algebra on homogeneous trees and relations with Toeplitz and Hankel operators

Author: Janusz Wysoczański
Journal: Proc. Amer. Math. Soc. 122 (1994), 1203-1210
MSC: Primary 46J30; Secondary 05C05, 47B35, 47D30
MathSciNet review: 1213871
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Abstract: We consider the Hecke algebra on homogeneous trees. We prove that it is a maximal abelian subalgebra of some operator algebras if the degree of the tree is greater than 2. There we show the influence of geometry of the tree on that fact. If the degree is 2 (for example, in the case of integers) then we show that operators which commute with the Hecke algebra can be uniquely represented as a sum of Hankel and Toeplitz matrices.

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Keywords: Hecke algebra, maximal abelian subalgebra, homogeneous tree, Hankel and Toeplitz matrices
Article copyright: © Copyright 1994 American Mathematical Society

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